My first thought is that the movement is not pixel-perfect.
Let's say your games resolution is 640x360, but it is scaled up to 1920x1080. When the sprite moves, the pixels on the sprite move at a subpixel level (essentially occupying space between two pixels), causing a visual effect that appears to be jitter. Now, this is just speculation, and may be totally wrong. But if this is the case, a way to fix it in unity would to draw your scene to a render texture.